CArtesian sampling with Variable density and Adjustable temporal resolution (CAVA)

Abstract

Purpose:

To develop a variable density Cartesian sampling method that allows retrospective adjustment of temporal resolution for dynamic MRI applications and to validate it in real-time phase contrast MRI (PC-MRI).

Theory and Methods:

The proposed method, called CArtesian sampling with Variable density and Adjustable temporal resolution (CAVA), begins by producing a sequence of phase encoding indices based on the golden ratio increment. Then, variable density is introduced by nonlinear stretching of the indices. Finally, the elements of the resulting sequence are rounded-up to the nearest integer. The performance of CAVA is evaluated using PC-MRI data from a pulsatile flow phantom and real-time, free-breathing data from ten healthy volunteers.

Results:

CAVA enabled image recovery at various temporal resolutions that were selected retrospectively. For the pulsatile flow phantom, image quality and flow quantification accuracy from CAVA were comparable to that from another pseudo-random sampling pattern with fixed temporal resolution. In addition, flow quantification results based on CAVA were in a good agreement with a breath-held segmented acquisition.

Conclusions:

By allowing retrospective binning of the MRI data, CAVA provides an avenue to retrospectively adjust the temporal resolution of PC-MRI.

Introduction

Cardiovascular MRI (CMR) is a powerful tool to assess a wide range of cardiac conditions. A typical CMR exam includes numerous breath-held segmented acquisitions with Cartesian sampling. However, breath-held segmented imaging (BSI) has several limitations. First, patients with cardiovascular disease can have severely limited capability to hold their breath (1). Second, BSI uses data acquired from multiple heartbeats to reconstruct a single heart cycle; this can lead to image artifacts in patients with arrhythmia. Third, respirophasic changes in cardiac function, which have been linked to constrictive physiology (2), cannot be characterized using BSI.

Free-breathing real-time imaging (FRI) can overcome limitations from arrhythmias or a patient’s ability to breath-hold (3, 4, 5). However, to generate images with sufficient temporal resolution, FRI data acquisition must be highly accelerated. Regularized reconstruction methods, such as compressed sensing (CS) with Cartesian or non-Cartesian acquisition, have been successfully applied to accelerate FRI for different CMR applications (6, 7). With typical TR values in the 4 to 5 ms range and the requirement to measure data with at least two velocity encodings, FRI for phase contrast MRI (PC-MRI) demands acceleration rates that are higher compared to other CMR applications, such as balanced SSFP-based FRI cine. For example, for a temporal resolution of 50 ms, balanced SSFP cine with TR of 2.5 ms can afford 20 readouts for each cardiac phase, while GRE-based PC-MRI with TR of 5 ms can only afford 5 readouts for each cardiac phase, leading to acceleration rates that are four times higher for PC-MRI. Therefore, for PC-MRI, FRI has only been possible using EPI acquisition (8) or radial acquisition with regularized reconstruction (9). More recently, golden angle-based radial samplings have gained popularity for dynamic MRI applications (10, 11). Two key advantages of such samplings are their ability to preferentially sample central k-space and to maintain sampling uniformity across different time scales, which allows retrospective adjustment of temporal resolution.

Despite the advantages offered by non-Cartesian acquisitions, single-echo Cartesian sampling remains the most commonly utilized clinical acquisition scheme due to its robustness to system imperfections and a long track record of success. Recently, it has been demonstrated that by advancing the phase encoding index by the golden ratio (12), conventional single-echo Cartesian acquisitions can enable retrospective adjustment of temporal resolution; however, the resulting sampling patterns lack variable density. Considering that most signal energy resides in central k-space, high acceleration is not feasible without preferentially sampling the central region of k-space. Recently, Li et al. (13) and we (14) independently proposed golden ratio-based Cartesian samplings that not only allow retrospective adjustment of the temporal resolution but also provide variable density.

In this work, we describe a Cartesian data sampling scheme, called CArtesian sampling with Variable density and Adjustable temporal resolution (CAVA). Distinguishing features of CAVA include: (i) temporal resolution that can be adjusted retrospectively, (ii) variable density to preferentially sample central k-space at a higher rate, (iii) maintaining incoherence, and (iv) ensuring a fully sampled time-averaged k-space to facilitate sensitivity map estimation. This work differs from that by Li et al. (13) in addressing features (ii) and (iv). The sampling pattern here is governed by adjustable parameters controlling local sample density, in contrast to the inflexible pattern in (13), which devotes over 10 percent of samples to one central k-space location. The results here also evaluate imaging performance for prospective sampling from ten healthy volunteers, in contrast to simulated data from a digital phantom considered in (13).

Theory

Generating CAVA

In this section, we describe generation of a CAVA sampling pattern on a k-space grid with N phase encoding (PE) steps. Two real-valued positive parameters, s and α, provide the flexibility to adjust the sampling density of the resulting pattern. The first step is to generate a sequence of indices on a smaller grid of size N_s = round(N/s). Starting from a randomly selected first PE index, p_s(1), the PE indices of the subsequent readouts are sequentially advanced by gN_s, yielding

$$p_s(i+1)=\langle p_s(i)+g{N}_s{\rangle }_{N_s},$$ [1]

where p_s(i) represents the PE index of the i^th sample on the grid of size N_s, $g=(\sqrt{5}-1)∕2$ is the golden ratio, and ⟨ · ⟩_Ns represents remainder modulo N_s. In the second step, the samples p_s(i) are mapped to a larger grid using a nonlinear stretching operation, yielding

$$p(i)=p_s(i)-c\text{sign}\left(\frac{N_s}{2}-p_s(i)\right){\mid \frac{N_s}{2}-p_s(i)\mid }^{\alpha }+\frac{N-N_s}{2},$$ [2]

$$p_c(i)=\lceil p(i)\rceil ,$$ [3]

where: P_c(i) is the PE index of the i^th CAVA sample on the grid of size N; s controls the relative acceleration rate at central k-space, with s > 1 ensuring that the sampling density is higher at the center of k-space; α ≥ 0 controls the transition from higher density central region to a lower density outer region; ⌈x⌉ denotes the smallest integer greater than or equal to x; and $c=\frac{N-N_s}{2^{(1-\alpha )N_s^{\alpha }}}$ maps p_s = 1 and p_s = N_s to p = 1 and p = N, respectively. The values of s and α can be adjusted to control the sampling density profile along the PE direction. For a given net acceleration rate, the central k-space has sampling density roughly s > 1 times greater than the full k-space average. In this work, we selected s = α = 3. Figure 1 depicts the nonlinear stretching process from the smaller N_s-point grid to the final N-point grid. Figure 2 highlights the dependence of CAVA sampling density on the values of s and α.

Figure 1:

Depiction of the nonlinear stretching employed in CAVA. First, a phase encoding sequence, p_s(i), is generated on a smaller grid by adding the golden ratio offset from one sample to the next (Eq. 1). Then, each element of the sequence is vertically stretched to generate p(i) (Eq. 2). Here, N=90, N_s=30, α = 3, and s = 3. Only 16 samples are shown.

Figure 2:

Impact of α and s values on the sampling density. (a) CAVA patterns from six different combinations of α and s are shown. (b) Sampling frequency when α is varied and s is fixed at 2. (c) Sampling frequency when α is varied and s is fixed at 3. Here, N = 90.

Due to the golden ratio jumps in k-space, CAVA sampling patterns can be re-binned to yield different temporal resolutions without sacrificing the uniformity of the sampling in each frame. Figure 3a shows re-binning of the same CAVA sampling pattern, providing different temporal resolutions. An additional benefit of CAVA is that when k-space data are averaged over time, they produce fully sampled k-space, given that a sufficient number of PE lines are acquired. For N = 90 and a fully sampled frequency encoding dimension of size 128, Figure 3c compares the time-averaged k-space for 10, 100, and 1,000 acquired k-space lines. After collecting 100 lines, the central 30 PE indices are sampled at least once, and after collecting 1,000 lines, all 90 PE indices are sampled at least once. The resulting fully sampled, time-averaged k-space can be used to estimate sensitivity maps for SENSE-based techniques or interpolation kernels for GRAPPA or SPIRiT.

Figure 3:

Example CAVA sampling patterns. (a) Retrospective adjustment of temporal resolution with CAVA. All sampling patterns were generated from the same sequence of phase encoding indices. The resolution was retrospectively changed by assigning different number of lines per frame (LPF). (b) The composite sampling pattern is a union of two independent CAVA patterns, with one used to collect compensated data and the other used to collect velocity encoded data. (c) The time-averaged CAVA pattern after acquiring 10 lines. (d) The time-averaged CAVA pattern after acquiring 100 lines. (e) The time-averaged CAVA pattern after acquiring 1,000 lines.

To extend this sampling method to PC-MRI, we create two different CAVA sampling patterns, one for the velocity-compensated measurements and one for the velocity-encoded measurements. To avoid sampling the same PE indices and to ensure that the two patterns interleave, the starting point, p_s(1), for velocity-encoded measurements was shifted by gN_s/2 with respect to the starting point of the velocity-compensated measurements. An example CAVA sampling pattern for PC-MRI is shown in Figure 3b.

Methods

Data Acquisition from a Pulsatile Flow Phantom

A pulsatile flow phantom experiment was performed to acquire fully sampled PC-MRI data at high temporal resolution. The pulsatile flow was applied to a pipe, with inner diameter of 5/8 inch, placed in a U-shape arrangement inside the magnet bore. Two water bottles supported the pipe, as shown in Figure 4. The imaging plane was approximately perpendicular to the flow direction. All data were acquired using a 1.5 T (MAGNETOM, Avanto, Siemens Healthcare, Erlangen, Germany) scanner with 18-channel cardiac array. A total of eight fully sampled data sets were collected, each with a different pulsatile waveform set using a programmable pump (MR 5000 by Shelley Medical Imaging Technologies, Toronto, Ontario, Canada). In addition to the shape of the waveform, the duration of the pulsatile cycle was varied between 750 ms and 1,200 ms across the eight acquisitions. The data were collected with prospective triggering using a traditional GRE-based sequence, with flow-encoded and flow-compensated readouts interleaved. To maintain high temporal resolution, segment size was selected to be one, i.e., one velocity encoded and one velocity compensated readouts were recorded in each segment. With TR = 5.13 ms, it led to a temporal resolution of 10.26 ms. The other relevant scan parameters were: TE = 3.18 ms, flip angle = 15°, acquisition matrix = 90 × 144, FOV = 178 × 280 mm, scan time = 68 to 108 s, VENC = 150 cm/s, slice thickness = 8 mm, acquisition bandwidth = 503 Hz/pixel, and asymmetric echo off. The data were retrospectively undersampled with two Cartesian sampling patterns: VISTA (15) and CAVA. VISTA is a variable density pseudorandom sampling pattern that is based on Riesz energy minimization. Starting from a random initialization, VISTA iteratively updates the sampling pattern to maximize separation among the neighboring samples. VISTA allows variable density but does not permit retrospective adjustment of temporal resolution. We recently extended VISTA for PC-MRI (16). Using VISTA and CAVA patterns, the undersampling process was repeated to simulate six different readout lines per frame (LPF), i.e., LPF (k) = 4, 5, 6, 8,10, and 15, leading to temporal resolutions (2 × k × TR) of 41.0, 51.3, 61.6, 82.1, 102.6, and 153.9 ms, respectively. To mimic the real-time acquisition, only one readout was selected from each fully sampled frame. For example, the first CAVA index was picked from the first fully sampled frame, the second CAVA index was picked from the second frame and so forth. For CAVA, only one sampling pattern was used, and different temporal resolutions were realized by binning k consecutive samples into one temporal frame. In contrast, for VISTA, a separate sampling pattern was generated for each temporal resolution. Since exact realizations of CAVA and VISTA depend on the starting point, p_s(1), and initial distribution of samples, respectively, the retrospective undersampling process was repeated for three different randomly selected values of p_s(1) for CAVA and three random initializations for VISTA.

Figure 4:

Pulsatile flow phantom (a) A slice showing a cross-section of two large water bottles and the tubes carrying pulsatile flow in opposite directions. The regions of interest used to quantify peak velocity and stroke volume (ROI-1 and ROI-2) as well as rSNR (ROI-3) are identified. (b) The velocity image corresponding to the magnitude image shown in (a). (c) Flow rate in ROI-2 for two (out of eight) different waveforms.

Data Acquisition from Healthy Volunteers

To further evaluate the performance of CAVA, PC-MRI data were collected from 10 healthy volunteers. All data were acquired using a 3 T (MAGNETOM, Prisma, Siemens Healthcare, Erlangen, Germany) scanner with 48-channel cardiac array. Each volunteer was imaged with both fully sampled BSI and FRI CAVA acquisition. The data were collected using a traditional GRE-based sequence, with flow-encoded and flow-compensated readouts interleaved. BSI data were collected with retrospective triggering, while the CAVA data were collected continuously for 10 s. The order of two acquisitions was randomized across volunteers. The imaging plane was prescribed perpendicular to the ascending aorta above the aortic valve. The other relevant scan parameters were: TR = 4.21 ms, TE = 2.12 ms, flip angle = 15°, acquisition matrix = 84 × 128, FOV = 250 × 300 mm, CAVA scan time = 10 s, VENC = 150 cm/s, slice thickness = 6 mm, acquisition bandwidth = 698 Hz/pixel, and asymmetric echo on. The data from each CAVA scan were retrospectively re-binned to create six data sets with 4, 5, 6, 8, 10, and 15 LPF (k) for temporal resolutions of 33.7, 42.1, 50.5, 67.4, 84.2, and 126.3 ms, respectively. For BSI, the relevant scan parameters were: TR = 4.64 ms, TE = 2.47 ms, acquisition matrix = (108 − 131) × (144 − 176), FOV = (230 − 282) × (280 − 340) mm, VENC = 150 cm/s, slice thickness = 6 mm, acquisition bandwidth = 451 Hz/pixel, isotropic image resolution = 1.7 — 1.9 mm, and temporal resolution = 37.1 ms. To highlight the impact of respiration on FRI flow quantification, we additionally collected a CAVA data set from one of the healthy volunteers over a span of 27 s under deep breathing conditions.

Image Recovery and Analysis for Pulsatile Flow Phantom

To reconstruct the accelerated CAVA data sets, the recently proposed ReVEAL (17, 18) technique was used. ReVEAL exploits wavelet sparsity as well as magnitude and phase similarities across velocity encodings to jointly reconstruct the velocity encoded and velocity compensated images. ReVEAL introduces three tuning parameters. The first parameter, λ, controls the regularization strength for wavelet domain sparsity. The second parameter, ω, represents the variance of noise in k-space. The third parameter, σ, represents a measure of magnitude and phase similarity across velocity encodings. The k-space noise variance, ω, was estimated from the outer portions of k-space. The other two parameters were tuned by subjectively evaluating the image quality from a single CAVA data set with k = 6. The parameter values were held constant for all pulsatile waveforms, sampling realizations, and temporal resolutions. ReVEAL was implemented in custom Matlab software (Mathworks, Natick, MA) and run offline on an Windows 7 PC equipped with a Tesla K40c GPU (Nvidia, Santa Clara, CA). The software utilizes GPU acceleration for a runtime of approximately 3 minutes. Open source software for ReVEAL is available online at GitHub¹. Coil sensitivity maps were estimated using ESPIRiT (19). The reconstructed image series were converted to DICOM, and the cross-section of the pipes was then segmented using Segment software (20). The peak velocity (PV), stroke volume (SV), and recovery signal-to-noise ratio (rSNR) for each waveform and sampling realization were defined as follows:

$${\text{SV}}_{i,j}^k=\text{Stroke Volume:}{i}^{\text{th}}\text{Sampling},j^{\text{th}}\text{Waveform},\text{LPF}=k$$ [4]

$${\text{PV}}_{i,j}^k=\text{Peak Velocity:}{i}^{\text{th}}\text{Sampling},j^{\text{th}}\text{Waveform},\text{LPF}=k$$ [5]

$$\begin{gathered} {\text{rSNR}}_{i,j}^k=-20{\log }_{10}[\frac{\Vert {\widehat{x}}_{i,j}^k-x_j^k\Vert }{\Vert x_j^k\Vert }] \\ \text{for}i=1,2\dots ,Ij=1,2\dots ,Jk=4,5,6,8,10,15, \end{gathered}$$ [6]

where ${\widehat{x}}_{i,j}^k$ represents images reconstructed using ReVEAL from undersampled data, and $x_j^k$ represents fully sampled images with temporal resolution matched to that of ${\widehat{x}}_{i,j}^k$. To generate $x_j^k$ images, k consecutive frames of the original high-resolution images were averaged. We refer to these fully sampled images with matched resolution as FS-MR. To assess variability of SV and PV in images recovered from CAVA and VISTA data sets, normalized values of SV and PV were calculated as a percentage of the reference values, yielding

$${\text{NSV}}_{i,j}^k=\frac{{\text{SV}}_{i,j}^k}{{\text{SVREF}}_j}\times 100$$ [7]

$$\begin{gathered} {\text{NPV}}_{i,j}^k=\frac{{\text{PV}}_{i,j}^k}{{\text{PVREF}}_j}\times 100 \\ \text{for all}i,j,\text{and}k, \end{gathered}$$ [8]

where PVREF_j and SVREF_j represent peak velocity and stroke volume, respectively, calculated from the fully sampled high-resolution reference. For both CAVA and VISTA, t-tests (α = 0.05) were performed to compare ${\text{NSV}}_{i,j}^k$ and ${\text{NPV}}_{i,j}^k$ to the reference value of 100. The values of ${\text{rSNR}}_{i,j}^k$ from CAVA and VISTA were also compared to each other using t-test (α = 0.05). For each k value, the t-test was performed by aggregating all entries for different i and j values. Due to observable difference in the flow profiles, the two cross-sections (ROI-1 and ROI-2 shown in Figure 4) of the pipe were treated separately, leading to 16 “waveforms.” Therefore, for SV and PV, J = 16, and for rSNR, J = 8. To emphasize contributions from dynamic regions, ROI-3 was used to calculate rSNR, as shown in Figure 4.

Image Recovery and Analysis for Healthy Volunteers

The accelerated CAVA data sets were reconstructed using ReVEAL. The reconstructed image series were converted to DICOM, and the aortic cross-section was then segmented using Segment software. The PV and SV values for each heartbeat were calculated and compared against the fully sampled BSI reference.

For flow quantification, we define the following parameters

$${\text{SV}}_{i,j}^k=\text{Stroke Volume:}{i}^{\text{th}}\text{Heartbeat},j^{\text{th}}\text{Volunteer},\text{LPF}=k$$ [9]

$$\begin{gathered} {\text{PV}}_{i,j}^k=\text{Peak Velocity:}{i}^{\text{th}}\text{Heartbeat},j^{\text{th}}\text{Volunteer},\text{LPF}=k \\ \text{for}i=1,2,\dots ,Ij=1,2,\dots ,Jk=4,5,6,8,10,15. \end{gathered}$$ [10]

To assess variability of SV and PV in images recovered from CAVA data sets, normalized values of SV and PV were calculated as a percentage of the reference values, yielding

$${\text{NSV}}_{i,j}^k=\frac{{\text{SV}}_{i,j}^k}{{\text{SVREF}}_j}\times 100$$ [11]

$$\begin{gathered} {\text{NPV}}_{i,j}^k=\frac{{\text{PV}}_{i,j}^k}{{\text{PVREF}}_j}\times 100 \\ \text{for all}i,j,\text{and}k, \end{gathered}$$ [12]

where PVREF_j and SVREF_j are the peak velocity and stroke volume for the j^th volunteer calculated from the BSI reference. In addition, t-tests (α = 0.05) were performed to compare ${\text{NSV}}_{i,j}^k$ and ${\text{NPV}}_{i,j}^k$ values from all heartbeats (i) and volunteers (j) to the reference value of 100. The t-test was separately performed for each value of k.

Results

In the first study, we collected and processed PC-MRI data for a pulsatile flow phantom. To create a high quality reference, we collected eight fully sampled data sets, each with a different flow waveform. For SV and PV quantification, the high temporal resolution images served as a reference, while, for rSNR quantification, FS-MR images served as a reference. The quantitative results are shown in Figure 5. The bars represent mean values while the error bars represent ±std. For each value of k, mean±std were calculated from all waveforms (j) and sampling realizations (i). Table 1 summarizes the mean values shown in Figure 5 and additionally provides t-test results. The overall performances of CAVA and VISTA were comparable, with VISTA exhibiting slight advantage in terms of rSNR. The advantage of VISTA was within 0.5 dB for k ≤ 10; only at k = 15, VISTA had larger than 0.5 dB advantage. For NSV, the quantification from VISTA and CAVA were comparable. Although the NSV values from VISTA and CAVA were statistically different for k = 8 and k = 10, the largest difference (0.860 at k = 10) between the mean NSV values from VISTA and CAVA was less than 1% of the reference. The NSV values from both methods were statistically different (except for VISTA at k = 15) from the high-resolution fully sampled reference, but their mean values were within 4% of the reference. For NPV, the quantification of VISTA and CAVA were comparable, with CAVA exhibiting slight underestimation compared to VISTA. The mean difference between CAVA and VISTA was within 2% for k ≤ 8 but grew to over 5% for k = 15. Also, the NPV values for both methods were statistically different from the high-resolution fully sampled reference but, except for CAVA at k = 15, were within 10% of the reference on average.

Figure 5:

Flow quantification and recovery SNR results from the pulsatile flow phantom. (a) Recovery SNR (rSNR) for VISTA and CAVA for eight different flow waveforms (j) and three realizations (i) of the sampling pattern. (b) Normalized SV across 16 different waveforms (eight from ROI-1 and eight from ROI-2) and three different sampling realizations. (c) Same comparison as (b) but for normalized PV. The results are presented as mean±std for different temporal resolutions, k.

Table 1:

Flow and rSNR quantification for phantom data. Each entry represents the mean (across i and j) of the difference between CAVA and VISTA, CAVA and Ref. or VISTA and Ref. Here, Ref. corresponds to the fully sampled high-resolution image series.

k	4	5	6	8	10	15
rSNR
CAVA–VISTA	0.011	−0.078	−0.226	−0.355	−0.192	−0.650
t-test	0	1	1	1	1	1
NSV
CAVA–VISTA	0.468	0.394	0.026	−0.631	0.860	−0.740
t-test	0	0	0	1	1	0
CAVA–Ref.	−3.156	−1.975	−1.596	−2.268	−0.430	−1.545
t-test	1	1	1	1	1	1
VISTA–Ref.	−3.625	−2.369	−1.622	−1.637	−1.290	−0.805
t-test	1	1	1	1	1	0
NPV
CAVA–VISTA	−0.500	−1.114	0.815	−0.941	−2.070	−5.114
t-test	0	1	0	0	1	1
CAVA–Ref.	−6.32	−5.157	−6.002	−8.036	−8.587	−11.61
t-test	1	1	1	1	1	1
VISTA–Ref.	−5.827	−4.043	−6.818	−7.095	−6.517	−6.493
t-test	1	1	1	1	1	1

To demonstrate the application of CAVA to real-time PC-MRI, we compared SV and PV from FRI CAVA with that from BSI using data from healthy volunteers. Figure 6 provides quantification for NSV and NPV from the prospectively undersampled data collected from 10 volunteers. Here, the value of 100 represents quantification from BSI data sets. For each value of k, mean±std were calculated from all volunteers (j) and heartbeats (i). Table 2 summarizes the results shown in Figure 6 and additionally provides t-test results. For NSV, there in good agreement between CAVA and BSI reference for k ≤ 15, with the largest discrepancy between the mean values less than 3%. At k = 15, the in vivo images exhibit strong artifacts (Figure 7) due to model mismatch, leading to overestimation and wider spread in NSV. As was the case with the phantom data, NPV underestimation is more pronounced at lower temporal resolutions. The underestimation, however, stays within 5% except for k = 15.

Figure 6:

Flow quantification results compiled from 10 healthy volunteers. For each LPF, the NSV (a) and NPV (b) values for all heartbeats (i) from all volunteers (j) are presented using mean±std.

Table 2:

Flow quantification results for volunteer data. Each entry represents the mean of the difference between CAVA and BSI reference (Ref.)

k	4	5	6	8	10	15
NSV
CAVA–Ref.	−2.639	−0.982	0.246	1.989	1.036	9.064
t-test	1	0	0	0	0	1
NPV
CAVA–Ref.	−2.420	−1.996	−2.295	−3.006	−3.919	−6.535
t-test	1	1	1	1	1	1

Figure 7:

Data reconstructed using ReVEAL. (a) Selected frames from a single volunteer for LPF (k) = 4, 5, 6, 8, 10, 15, which correspond to temporal resolutions of of 33.7, 42.1, 50.5, 67.4, 84.2, 126.3 ms, respectively. (b) Peak velocity profiles from different LPF values. (c) Volumetric flow rate from different LPF values.

To visually assess image quality, representative image frames for a single volunteer are shown in Figure 7a. Both magnitude and phase images are shown for six different temporal resolutions, indexed by LPF. Figures 7b-7c show PV and volumetric flow profiles for 4 consecutive heartbeats for different LPF values. Figure 8 highlights the potential impact of respiration on free-breathing CAVA images. The chest wall displacement observed from the reconstructed image series was used as a surrogate for respiratory motion.

Figure 8:

An example of physiological changes in SV as a function of breathing cycle. The volumetric flow rate for a volunteer over 27 seconds is shown in blue. An estimate of the chest wall motion is given in red. The SV decreases during inspiration, which is consistent with earlier studies.

Discussion

For MRI, non-Cartesian trajectories can offer several advantages, including variable density and incoherent artifacts. A variable density pattern maximizes k-space signal-to-noise ratio for a given readout duration, and incoherent artifacts facilitate the application of CS. More recently, golden angle-based radial and spiral trajectories have been proposed for 2D real-time CMR (21, 11). These acquisition schemes provide the added flexibility of adjusting temporal resolution retrospectively. In contrast, existing Cartesian trajectories are not equipped to combine retrospective adjustment of temporal resolution and variable density. We have proposed a new sampling method, called CAVA, that successfully combines artifact incoherence, variable density that can be parametrically controlled, and ability to vary temporal resolution after the acquisition.

Data collection with CAVA, when combined with ReVEAL reconstruction, can allow highly accelerated real-time imaging. In this work, the combination of CAVA and ReVEAL enabled PC-MRI at acceleration rates as high as R = 22.5 (LPF=4). Previously, real-time PC-MRI at such high acceleration rates had only been possible with non-Cartesian acquisitions (22). Our validation study, although small, supports the feasibility of real-time PC-MRI with Cartesian sampling and retrospective adjustment of temporal resolution.

The rSNR results from the phantom data highlight that performance of CAVA, in terms of overall image quality, is comparable to that of VISTA. At the very low temporal resolution of 153.9 ms, however, rSNR of CAVA is lower by more than 0.5 dB. For flow quantification, the performances of VISTA and CAVA are comparable for k < 8, with CAVA exhibiting slightly higher underestimation of NPV for k ≥ 8. The slightly inferior performance of CAVA, especially at lower temporal resolutions, can be attributed to the sampling distribution that is only approximately uniform and can lead to samples that are clustered together as seen in Figure 3c, where three central lines appears to be clustered together. This clustering is more pronounced for larger values of LPF due to the overall higher sampling density. In the case of VISTA, the gap between neighboring readouts are regulated using an optimization framework that leads to more even coverage of k-space. However, unlike VISTA and other similar methods, CAVA allows retrospective adjustment of temporal resolution.

The quantitative results from volunteer imaging follow the results from phantom imaging. The NSV and NPV values for CAVA closely match the BSI values for k ≤ 10. As is the case for phantom imaging, a slight underestimation is observed in NSV at k = 4, which can be attributed to regularization-induced blurring at a high acceleration rate. CAVA also underestimates PV with respect to the high-resolution reference. The underestimation of in vivo data is smaller than the one observed for the phantom data. This can be attributed to the difference in the temporal resolution of the reference. For phantom, the reference has a temporal resolution of 10.26 ms, while it is 37.1 ms for in vivo. For phantom imaging, when the CAVA NPV values are compared to temporal resolution matched reference, FS-MR, the underestimation is reduced to less than 4% for all k. Another disparity between the two studies is that NSV at k = 15 is overestimated for the in vivo study, while no such overestimation is observed for the phantom study. We attribute this overestimation to image artifacts (Figure 7) due the intra-frame model mismatch at poor temporal resolution. In the case of phantom, however, due to the small number of dynamic pixels, the model mismatch-related artifacts are limited. Overall, both studies support the central premise that CAVA enables retrospective adjustment of temporal resolution without significant loss in performance for clinically acceptable temporal resolutions (k ≤ 6).

One limitation of this study is the comparison of end-expiration BSI with FRI. Several studies have demonstrated a reduction of left ventricular stroke volume during inspiration. For example, Thompson et al. (23) demonstrated that aortic flow peaked during expiration under free-breathing conditions. To highlight the dependence of cardiac output on respiration, we analyzed additional data from one healthy volunteer. The data were collected continuously for 27 s using CAVA sampling. To amplify the effect of inspiration, the volunteer was instructed to breath deeply during the scan. The images were reconstructed at a resolution of 50.5 ms. Figure 8 depicts volumetric flow rate profiles over the span of 27 s as well as the chest wall displacement estimated by registering magnitude images across different frames. As seen in this figure, our measurements suggest a decrease in cardiac output during inspiration, which is in agreement with previous studies (23, 24, 25, 26, 27). Although this modulation in cardiac output contributes additional variation in Figure 6 compared to Figure 5, it also highlights the potential of CAVA-based FRI to study respirophasic changes in cardiac function in patients with constrictive physiology (2). Another potential limitation is that the extension of CAVA to the balanced SSFP sequence can be problematic because in balanced SSFP large k-space jumps between two consecutive PE lines can lead to image artifacts (28). Future studies will focus on the clinical application of CAVA.

Conclusion

We have proposed a new sampling method, CAVA, that exhibits variable density and adjustable temporal resolution. CAVA provides a Cartesian alternative to the golden angle radial sampling and may benefit a wide range of dynamic MRI applications, including real-time PC-MRI.